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DivisorSigma




Mathematica Notation

Traditional Notation









Number Theory Functions > DivisorSigma[k,n] > Inequalities





http://functions.wolfram.com/13.05.29.0024.01









  


  








Input Form





6/Pi^2 < (DivisorSigma[1, n] EulerPhi[n])/n^2 < 1 /; n >= 2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox["6", SuperscriptBox["\[Pi]", "2"]], "<", FractionBox[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], " ", RowBox[List["EulerPhi", "[", "n", "]"]]]], SuperscriptBox["n", "2"]], "<", "1"]], "/;", RowBox[List["n", "\[GreaterEqual]", "2"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mn> 6 </mn> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &lt; </mo> <mfrac> <mrow> <mrow> <msub> <semantics> <mi> &#963; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Sigma]&quot;, DivisorSigma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <msup> <mi> n </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mn> 2 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> DivisorSigma </ci> <cn type='integer'> 1 </cn> <ci> n </ci> </apply> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <power /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <geq /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox["6", SuperscriptBox["\[Pi]", "2"]], "<", FractionBox[RowBox[List[RowBox[List["DivisorSigma", "[", RowBox[List["1", ",", "n"]], "]"]], " ", RowBox[List["EulerPhi", "[", "n", "]"]]]], SuperscriptBox["n", "2"]], "<", "1"]], "/;", RowBox[List["n", "\[GreaterEqual]", "2"]]]]]]


Date Added to functions.wolfram.com (modification date)





2002-12-18